(c) What do you mean by reliability and validity of tests ? What is the difference between reliability and validity of a test ?…

(c) Reliability and validity. Reliability is the consistency or stability of a test: if the same persons are retested under equivalent conditions, scores should be nearly the same. It reflects freedom from random error. Validity is the extent to which a test measures the construct or criterion it claims to measure; a valid test yields scores that are meaningfully related to the intended attribute. The difference is that reliability is a necessary but not sufficient condition for validity. A test can be highly reliable yet invalid if it consistently measures the wrong thing; a test that is not reliable cannot be valid, because random error prevents a stable relation with the intended attribute. If reliability is raised from 0.80 to 0.90 by lengthening the test, the Spearman–Brown prophecy formula gives the expected validity: r_new = r_old × √(R_new/R_old). The original validity of 0.60 at R = 0.80 has a reliability-corrected value of 0.60/√0.80 ≈ 0.67; applying the new reliability gives 0.67 × √0.90 ≈ 0.64, equivalently 0.60 × √(0.90/0.80) ≈ 0.636. Thus the expected validity coefficient rises to about 0.64.

(d) Population at t = 30. The rate of increase is treated as a relative rate, so dP/dt = P r(t) = P(0.01 + 0.0001t²). Separating variables gives dP/P = (0.01 + 0.0001t²)dt. Integrating, ln P = 0.01t + 0.0001t³/3 + C. At t = 0, P = 1,000,000, so C = ln(10⁶). Therefore P(t) = 10⁶ exp(0.01t + 0.0001t³/3). At t = 30, the exponent is 0.3 + 0.9 = 1.2, so P(30) = 10⁶ e^1.2 ≈ 3,320,117. The population grows from one million to about 3.32 million because the relative growth rate itself rises with t², so later periods add a larger proportion of the existing population.

(e) Malaria medicine allocation. For deciding the amount of medicine to be sent to a malaria-affected area, the Morbidity Prevalence Rate (MPR) should be used. MPR counts all existing cases—old and new—present in the population at a point or over a defined period. Medicine dispatch is a stock requirement: it must cover the number of persons who are currently diseased and need treatment, not merely those who become newly infected during a short interval. If MPR is high, the immediate treatment burden is high, so more antimalarials, rapid diagnostic tests, and supportive supplies are needed. If MPR is low, smaller quantities may suffice even if some new cases are appearing. This causal chain—prevalence identifies current patients, current patients determine drug consumption, and drug consumption determines the quantity to send—makes MPR the appropriate operational measure. In India, malaria case management under the National Malaria Elimination Programme uses RDTs and ACTs; the quantity of ACTs to be dispatched to a block should be based on prevalent cases requiring treatment at the time of dispatch.

MIR, by contrast, measures new cases arising over time. It is useful for understanding transmission dynamics, detecting outbreaks, and evaluating control measures. For example, in a district implementing the National Malaria Elimination Programme, a falling MIR after distribution of long-lasting insecticidal nets or indoor residual spraying would show that prevention is reducing new infections, even if MPR remains temporarily high because existing cases still need treatment. MIR can also guide future planning, such as estimating next season’s drug demand or targeting high-incidence blocks, but it should not be the sole basis for the immediate quantity of medicine to dispatch.

Reliability and validity distinguish stable measurement from meaningful measurement; the population equation shows how a time-varying relative rate compounds; and in public health, prevalence determines present treatment needs while incidence reveals the process generating future needs. Hence MPR is the correct basis for medicine allocation, with MIR retained for surveillance and control evaluation.